Journal
PHYSICAL REVIEW E
Volume 65, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.65.056202
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The structure of the Lyapunov spectra for the many-particle systems with a random interaction between the particles is discussed. The dynamics of the tangent space is expressed as a master equation, which leads to a formula that connects the positive Lyapunov exponents and the time correlations of the particle interaction matrix. Applying this formula to one- and two-dimensional models we investigate the stepwise structure of the Lyapunov spectra that appear in the region of small positive Lyapunov exponents. Long range interactions lead to a clear separation of the Lyapunov spectra into a part exhibiting stepwise structure and a part changing smoothly. The part of the Lyapunov spectrum containing the stepwise structure is clearly distinguished by a wavelike structure in the eigenstates of the particle interaction matrix. The two-dimensional model has the same step widths as found numerically in a deterministic chaotic system of many hard disks.
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